ECE580 Homework Assignments

Spring 2016

Assignment 1: Assigned January 15, 2016.
Due by 7:30pm January 22, 2016.

Problems 1.5, 3.3, 3.8 from the textbook.

Prove that that if $\Theta$ and $\Sigma$ are convex sets
and $\alpha$ and $\beta$ are real numbers,
$\alpha\Theta+\beta\Sigma$ is convex. (Pay attention to the details
of the proof. See the examples in the text.)

With the same definitions, prove that the set $\alpha\Theta\cap\beta\Sigma$ is convex.
(Be sure to consider all possible cases.)

Assignment 2: Assigned January 24, 2016.
Due by 7:30pm January 30, 2016.

Assignment 3: Assigned February 2, 2016.
Due by 7:30pm February 8, 2016.

Problems 6.1, 6.2, 6.9, 6.13, and 6.14 from the textbook.

Assignment 4: Assigned February 8, 2016.
Due by 7:30pm February 15, 2016.

Problems 7.10, 9.3, 9.4, 8.1, and 8.8 from the textbook.

Assignment 5: Assigned February 15, 2016.
Due by 7:30pm March 2, 2016.

Problems 10.10, 10.11, 11.1, and 11.7 from the textbook.

Assignment 6: Assigned March 9, 2016.
Due by 7:30pm March 23, 2016.

Problems 12.3, 12.8, 12.14, 12.19, and 12.32 from the textbook.

Assignment 7: Assigned March 23, 2016.
Due by 7:30pm March 30, 2016.

Problems 13.1, 13.5 from the textbook, plus the following problems: write scripts in Matlab to apply the Nelder-Mead algorithm and the PSO algorithm to find the minimizer of $f(x) = x_1 e^{-x_1^2 - x_2^2}$.

Problems 21.2(c), 21.5, 21.6, 21.7, 21.8, 21.17, 21.18,
21.19, and 21.20.
Turn in at least six of the above problems. Extra points will
be awarded for doing more than six. Note the figures in
Chapter 22 that show the geometry of problems 21.18 - 21.20.
Before solving these problem, use the figure to help you
determine the solutions so that you know what the answers
should be before you start.